Why did ML only become viable after Nvidia's chips were available?
There is a lot of factors for the boom of AI industry. What many people miss though is the boom has mostly been in the Machine Learning part of AI. This can be attributed to various simple reasons along with their comparisons during earlier times:


Mathematics:  The maths behind ML algorithms are pretty simple and known for a long time (whether it would work or not was not known though). During earlier times it was not possible to implement algorithms which require high precision of numbers, to be calculated on a chip, in an acceptable amount of time. One of the main arithmetic operations division of numbers still takes a lot of cycles in modern processors. Older processors were magnitude times slower than modern processors (more than 100x), this bottleneck made it impossible to train sophisticated models on contemporary processors.
Precision: Precision in calculations is an important factor in ML algorithms. 32 bit precision in processor was made in the 80's and was probably commercially available in the late 90's (x86), but it was still hella slow than current processors. This resulted in scientists improvising on the precision part and the most basic Perceptron Learning Algorithm invented in the 1960's to train a classifier uses only $1$'s and $0$'s, so basically a binary classifier. It was run on special computers. Although, it is interesting to note that we have come a full circle and Google is now using TPU's with 8-16 bit accuracy to implement ML models with great success.
Parallelization : The concept of parallelization of matrix operations is nothing new. It was only when we started to see Deep Learning as just a set of matrix operations we realized that it can be easily parallelized on massively parallel GPU's, still if your ML algorithm is not inherently parallel then it hardly matters whether you use CPU or GPU (e.g. RNN's).
Data: Probably the biggest cause in the ML boom. The Internet has provided opportunities to collect huge amounts of data from users and also make it available to interested parties. Since an ML algorithm is just a function approximator based on data, therefore data is the single most important thing in a ML algorithm. The more the data the better the performance of your model.
Cost: The cost of training a ML model has gone down significantly. So using a Supercomputer to train a model might be fine, but was it worth it? Super computers unlike normal PC's are tremendously resource hungry in terms of cooling, space, etc. A recent article on MIT Technology Review points out the carbon footprint of training a Deep Learning model (sub-branch of ML). It is quite a good indicator why it would have been infeasible to train on Supercomputers in earlier times (considering modern processors consume much lesser power and gives higher speeds).
Although, I am not sure but I think earlier supercomputers were specialised in "parallel+very high precision computing" (required for weather, astronomy, military applications, etc) and the "very high precison part" is overkill in Machine Learning scenario.


Another important aspect is nowadays everyone has access to powerful computers. Thus, anyone can build new ML models, re-train pre-existing models, modify models, etc. This was quite not possible during earlier times, 

All this factors has led to a huge surge in interest in ML and has caused the boom we are seeing today. Also check out this question on how we are moving beyond digital processors.